Chop it, place it in a glass jar and keep in the freezer. When you need some parsley, open the jar, take whatever you need and use as you would fresh parsley (it thaws in seconds), and replace the jar in the freezer for next time.

It is generally not recommended to keep herbs in oil unless you are also freezing them. There is a risk of botulism. If you do decide to try to preserve parsley in oil, here are some safe preparation guidelines from Health Canada: